One coin in a collection of 5 is rigged to have a probability of showing heads equal to 0.2. The rest are fair (probability 0.5). A coin is chosen at random from the lot and tossed 3 times. It turns up heads 3 times in a row. What is the probability that it is the rigged coin given that it showed heads in 3 out of 3 tosses?

Step-by-step explanation:

The probability of the chosen coin being rigged is .

It is also given that, the outcome is a head all the 3 times.

The probability that all the outcomes will be head is .

According to the question, the probability is .

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74