chance

A single coin is tossed 5 times. What is the probability of getting at least one head?

Consider solving this using complement. Probability of getting no head = P(all tails) = 1/32 P(at least one head) = 1 - P(all tails) = 1 - 1/32 = 31/32.

What is the probability of the occurrence of a number that is odd or less than 5 when a fair die is rolled.

Let the event of the occurrence of a number that is odd be 'A' and the event of the occurrence of a number that is less than 5 be 'B'. We need to find P(A or B). P(A) = 3/6 (odd numbers = 1,3 and 5) P(B) = 4/6 (numbers less than 5 = 1,2,3 and 4) P(A and B) = 2/6 (numbers that are both odd and less than 5 = 1 and 3) Now, P(A or B) = P(A) + P(B) - P(A or B) = 3/6 + 4/6 - 2/6 P(A or B) = 5/6.

a) A die is rolled, find the probability that the number obtained is greater than 4. b) Two coins are tossed, find the probability that one head only is obtained. c) Two dice are rolled, find the probability that the sum is equal to 5. d) A card is drawn at random from a deck of cards. Find the probability of getting the King of heart.

a) 2 / 6 = 1 / 3 b) 2 / 4 = 1 / 2 c) 4 / 36 = 1 / 9 d) 1 / 52

Two dice are rolled, find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13

0 1/12 1

A bag contains blue and red balls. Two balls are drawn randomly without replacement. The probability of selecting a blue and then a red ball is 0.2. The probability of selecting a blue ball in the first draw is 0.5. What is the probability of drawing a red ball, given that the first ball drawn was blue?

0.4

What is the probability of rolling a pair of fives with two dice?

1/36

A die is rolled thrice. What is the probability that the sum of the rolls is atleast 5.

212/216=.98

A box contains 4 chocobars and 4 ice creams. Tom eats 3 of them one after another. What is the probability of sequentially choosing 2 chocobars and 1 icecream?

Probability of choosing 1 chocobar = 4/8 = 1/2 After taking out 1 chocobar, the total number is 7. Probability of choosing 2nd chocobar = 3/7 Probability of choosing 1 icecream out of a total of 6 = 4/6 = 2/3 So the final probability of choosing 2 chocobars and 1 icecream = 1/2 * 3/7 * 2/3 = 1/7