Advertisements
Advertisements
Question
Five Students A, B, C, D, and E are competing in a long-distance race. Each student’s probability of winning the race is given below:
A → 20%, B → 22%, C → 7%, D → 15% and E → 36%
(i) Who is most likely to win the race?
(ii) Who is least likely to win the race?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
Solution
Given probabilities of five students A, B, C, D, and E such as
P(A) = 20%, P(B) = 22%, P(C) = 7%, P(D) = 15%, and P(E) = 36%
(i) The mostly chance of winning the race is of Student E. ..........[∵ P(E) = 36% maximun]
(ii) The least chances of winning the race is of Student C. ..........[∵ P(C) = 7% minimum]
(iii) The sum of the probabilities
= P(A) + P(B) + P(C) + P(D) + P(E)
= 20% + 22% + 7% + 15% + 36%
= 100%
(iv) Favourable outcomes that either A or D will win = 20% + 15% = 35%
P(either A or D will win) =`35/100=7/20`
(v) (a) Favourable outcomes that B will win = 22%
P(S) =`22/100=11/50`
(b) S' = B will not win the race.
(c) P(S') = 1 − P(S)
= `1-11/50=(50-11)/50=39/50`
APPEARS IN
RELATED QUESTIONS
A dice is thrown 20 times and the outcomes are noted as shown below:
| Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
| No. of times | 2 | 3 | 4 | 4 | 3 | 4 |
Now a dice is thrown at random, find the probability of getting:
A survey of 50 boys showed that 21 like tea while 29 dislike it. Out of these boys, one boy is chosen at random. What is the probability that the chosen boy
(i) likes tea
(ii) dislikes tea
A bag contains 4 white and 6 black balls,- all of the same shape and same size. A ball is drawn from the bag without looking into the bag. Find the probability that the ball drawn is:
(i) a black ball
(ii) a white ball
(iii) not a black ball
In a single throw of a dice, find the probability of getting a number 6
Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is 80
Suppose S is the event that will happen tomorrow and P(S) = 0.03. State in words, the complementary event S’.
Suppose S is the event that will happen tomorrow and P(S) = 0.03. Find P(S’)
A Ticket is randomly selected from a basket containing 3 green, 4 yellow, and 5 blue tickets. Determine the probability of getting:
(i) a green ticket
(ii) a green or yellow ticket.
(iii) an orange ticket.
A carton contains eight brown and four white eggs. Find the probability that an egg selected at random is:
(i) brown
(ii) white
The following table shows number of males and number of females of a small locality in different age groups.
| Age in years | 10-20 | 21-50 | Above 50 |
| Male | 8 | 12 | 6 |
| female | 6 | 10 | 4 |
If one of the persons, from this locality, is picked at random, what is the probability that
- the person picked is a male?
- the person picked is a female?
- the person picked is a female aged 21-50?
- the person is a male with age up to 50 years?
