Question

Shapes. Following suppose the probability that the shape lands flat (1 or 6) is p for some 0 spsi.

a) For each k = 1, 2,..., 6 find a formula for P(k) in terms of p.
b) Find a formula in terms of p for the probability that the number shown by the shape is 3 or more.

Answer 1

To find the probability of a shape landing flat on 1 or 6, you need to calculate P(A) in terms of p. The probability of the shape showing a number of 3 or more can be found using the complement rule.

Step-by-step explanation:

To find the probability of a shape landing flat on 1 or 6 (let's call this event A), we need to calculate P(A) in terms of p.

Since there are six possible outcomes when rolling a fair, six-sided die, the probability of any specific outcome is 1/6. The probability of the shape landing flat on 1 or 6 is P(A) = P(1) + P(6) = 1/6 + 1/6 = 2/6 = 1/3.

To find the probability of the shape showing a number of 3 or more (let's call this event B), we can use the complement rule. The complement of event B is the shape showing a number less than 3, which is the event of the shape showing 1 or 2. So, P(B) = 1 - P(1) - P(2) = 1 - 1/6 - 1/6 = 4/6 = 2/3.