Advertisements
Advertisements
Question
A coin is tossed 5 times. Find the probability of getting (i) at least 4 heads, and (ii) at most 4 heads.
Solution
Total number of the probability of tossing a coin 5 times is 32
(i) Probability of getting at least 4 heads
P(X=4) + P(X=5)
`""^5C_4 (1/2)^1 (1/2)^4 + ""^5C_5 (1/2)^0 (1/5)^5`
= `""^5C_4 (1/2)^5 + ""^5C_5 (1/2)^5`
= `6/32 = 3/16`
(ii) Probability of getting at most 4 head
P(X=1) + P(X=2) + P(X=3) + P(X=4)
`""^5C_1 (1/2)^5 + ""^5C_2 (1/2)^5 + ""^5C_3 (1/2)^5 + ""^5C_4 (1/2)^5`
= `(1/2)^5` [5+ 10 + 10 + 5]
= `(15)/(16)`
RELATED QUESTIONS
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
(i) 5 successes?
(ii) at least 5 successes?
(iii) at most 5 successes?
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and third card drawn is an ace?
If A and B are two events such that P (A ∩ B) = 0.32 and P (B) = 0.5, find P (A/B).
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
Mother, father and son line up at random for a family picture. If A and B are two events given by A = Son on one end, B = Father in the middle, find P (A/B) and P (B/A).
A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
The probability that a student selected at random from a class will pass in Mathematics is `4/5`, and the probability that he/she passes in Mathematics and Computer Science is `1/2`. What is the probability that he/she will pass in Computer Science if it is known that he/she has passed in Mathematics?
If A and B be two events such that P (A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A/B) .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (B/A) .
If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find P (A).
A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: p1 p2 .
A and B toss a coin alternately till one of them gets a head and wins the game. If A starts the game, find the probability that B will win the game.
The probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events : 'A passes', 'B passes' as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.
A card is drawn from a well-shuffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
(i) What is the probability that both the cards are of the same suit?
(ii) What is the probability that the first card is an ace and the second card is a red queen?
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among 100 students, what is the probability that: (i) you both enter the same section? (ii) you both enter the different sections?
A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out from the latter. Find the probability that the ball drawn is white.
When three dice are thrown, write the probability of getting 4 or 5 on each of the dice simultaneously.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
If one ball is drawn at random from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
Mark the correct alternative in the following question:
\[\text{ Let A and B are two events such that } P\left( A \right) = \frac{3}{8}, P\left( B \right) = \frac{5}{8} \text{ and } P\left( A \cup B \right) = \frac{3}{4} . \text{ Then } P\left( A|B \right) \times P\left( A \cap B \right) \text{ is equals to } \]
If A and B are two events such that A ≠ Φ, B = Φ, then
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A|B \right) = p, P\left( A \right) = p, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cup B \right) = \frac{5}{9}, \text{ then} p = \]
Mark the correct alternative in the following question:
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is
Mother, father and son line up at random for a family photo. If A and B are two events given by
A = Son on one end, B = Father in the middle, find P(B / A).
