1. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is either red or king.

a. 1/4

b. 7/13

c. 15/26

d. 8/13

## EXPLANATION

Red possibility = 26

King possibility (After eliminating red cards) = 2

Total = 26+2 = 28

Possibility = 28 / 52 = 7/13

2. Six dice are thrown simultaneously. Find the probability that all of them show the same face.

a. 1/6

b. 1/6^{6}

c. 1/36

d. 1/6^{5}

## EXPLANATION

Total = 6^{6}

Possibility = 6/6^{6} = 1/6^{5}

3. If you have 3 tickets to a lottery for which 10 tickets were sold and 5 prizes are to be given, the probability that you will win at least one prize is

a. 11/12 ⁄

b. 3/10

c. 1/2

d. 3/50

## EXPLANATION

Total number of ways to select 5 tickets out of 10 tickets = ^{10}C_{5}

Total number of ways to select 5 tickets out of 7 remaining tickets (after selecting your 3 tickets) = ^{7}C_{5}

Probability of winning at least one prize = 1 – Probability of not winning any prize

Probability of not winning any prize = (number of ways to select 5 tickets out of 7 remaining tickets) / (number of ways to select 5 tickets out of 10 tickets) = ^{7}C_{5} / ^{10}C_{5} = (7*6) / (5*4) = 21/50

Therefore, Probability of winning at least one prize = 1 – 21/50 = 29/50 = 11/12

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