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प्रश्न
One coin and a die are thrown simultaneously. Find the probability of the following event:
Event A: To get a head and a prime number.
उत्तर
One coin and a die are thrown simultaneously.
Sample space,
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
∴ n(S) = 12
Event A: To get a head and a prime number.
∴ A = {(H, 2), (H, 3), (H, 5)}
∴ n(A) = 3
∴ P(A) = `("n"("A"))/("n"("S"))`
∴ P(A) = `3/12`
∴ P(A) = `1/4`
The Probability of event A is `1/4`.
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संबंधित प्रश्न
If two coins are tossed, find the probability of event getting head on both the coins
If two dice are rolled simultaneously, find the probability of the following events.
Event A: The sum of the digits on the upper faces is at least 10
A box contains 5 strawberry chocolates, 6 coffee chocolates and 2 peppermint chocolates. If one of the chocolates is picked from the box at random, find the probability of the following events by completing the activity.
Activity : Let ‘S’ is the sample space.
∴ n(S) = 5 + 6 + 2 = 13
Event B: it is a peppermint chocolate.
∴ n(B) = `square`
∴ P(B) = `square/("n"("S"))` .......[Formula]
P(B) = `square/13`
In the adjoining figure, the arrow rests on any number, after the rotation of the disc. The probability that it will rest on any of the numbers on the disc is equal. Let A be any random event. To find the probability of A, fill in the boxes.
(1) S = `square`
(2) n(S) = `square`
(3) Let A be the event that arrow points at the number which is perfect cube.
A = `square`
∴ n(A) = `square`
(4) ∴ P(A) = `(n(A))/(n(S)) = square/square = square`
Using the digits 0, 2, 3, 5 the two-digit numbers are constructed without repetition of digits. Find the probability of the following events:
Condition for event A: The number formed is even.
Let E be an event and P(E) = `6/7`, then find the value of P(not E).
An urn contains 12 red balls, 15 yellow balls and 18 blue balls. A ball is choosen at random, then to find the probability of choosing a blue and red coloured balls, fill in the boxes.
Total number of balls = 12 + `square` + `square` = `square`
(1) Let E be the event that the choosen ball is blue.
Number of blue balls = `square`
Thus,
P(E) = `"Number of blue balls"/"Total number of balls"`
= `square/square`
(2) Let F be the event that the choosen ball is red.
Number of red balls = `square`
Thus,
P(F) = `square/"Total number of balls"`
= `square/square`
A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. If the probability that the number formed is divisible by 4, is P, then 5P is ______.
A man has 3 pairs of white socks and 2 pairs of blue socks kept together in a bag. If he dressed up hurriedly in the dark, the probability that after he has put on a white sock, he will then put on another white sock is `M/n` (`M/n` is in simplest form) then n – M = ______.
A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability of the following events?
Event A : The number formed is an odd number.
Event B : The number formed is a multiple of 5.
