Question

Steve has 11 biscuits in a tin.

There are 4 digestive, 5 chocolate and 2 ginger biscuits.
Steve takes two biscuits at random from the tin.
Work out the probability that he chooses two different types of biscuits.

Answer 1

The probability of Steve choosing two different types of biscuits from the tin is 38/55 or 0.69.

Step-by-step explanation:

To find the probability of Steve choosing two different types of biscuits, we need to calculate the probability of choosing one digestible and one chocolate biscuit, one digestible and one ginger biscuit, and one chocolate and one ginger biscuit.

The total number of possible combinations of two biscuits is given by the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of biscuits and r is the number of biscuits being chosen. In this case, n = 11 and r = 2, so C(11, 2) = 55.

The number of different combinations of biscuits can be calculated by summing the combinations of choosing one biscuit of each type: C(4, 1) * C(5, 1) + C(4, 1) * C(2, 1) + C(5, 1) * C(2, 1) = 20 + 8 + 10 = 38.

Therefore, the probability of Steve choosing two different types of biscuits is 38/55 or 0.69 (rounded to two decimal places).