Question

You pick a card at random, put it back, and then pick another card at random. 3 4 5 6 7 What is the probability of picking a divisor of 6 and then picking a number less than 5? Simplify your answer and write it as a fraction or whole number.

Answer 1

Probability = required outcome /all possible outcome

You have 5 cards on the deck. The exercise has reposition, i.e. you put the card back into the deck before picking the next one, so the total number of cards is always 5.

all possible outcome = 5

Divisor of 6 = 3, 6

Probability of picking a divisor of 6 = 2/5

Number less than 5 are : 3 and 4 = 2/5

The intersection between both events is equal to the product of both probabilities since the events are independent.

The probability of picking a divisor of 6 and then picking a number less than 5 is:

P(divisor of 6) and P(no.less than 5) = 2/5 * 2/5 = 4/25