There are two newborns, Gary and Eric. The future lifetime of Gary is uniformly distributed between 0 to 60 years. The future lifetime of Eric is uniformly distributed between 0 to 40 years. Their future lifetimes are independent. Calculate the probability that Gary dies first

Answers

Answer 1

Answer:

Answer:

$\text{The probability that Gary dies first = }(1)/(3)$

Step-by-step explanation:

To find the required probability,

We can split the 40 years of Eric into very small pieces of time dt. Now, If Eric dies at time t and Gary dies before Eric, the probability is :

$(t)/(60)* (dt)/(40)=(t\cdot dt)/(2400)$

Hence the probability that Gary dies first is given by :

$=\int_(0)^(40)(t)/(2400)dt \n\n= (1)/(3)$

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Jason has a piece of wire that is 62.4 inches long. He cuts the wire into 3 equal pieces. Which is the best estimate of the length of each piece of wire.

Answers

Answer:

The best estimate of the length of each piece of wire is 20.8 inches (Approx).

Step-by-step explanation:

Let us assume that the length of each pieces of wire be x.

As given

Jason has a piece of wire that is 62.4 inches long.

He cuts the wire into 3 equal pieces.

Than the equation becomes

3x = 62.4

$x = (62.4)/(3)$

x = 20.8 inches (Approx)

Therefore the best estimate of the length of each piece of wire is 20.8 inches (Approx).

62.4/3=20.8 is one of the 3 wires that are equal

Given the following scenario, decide if it is a permutation or combination, and then calculate the possibilities. Papa John’s pizza has 17 different toppings to choose from. In how many ways can you make a three topping pizza?

Answers

It is a combination because the order in which the toppings are used does not change the result.

The formula of combination is C 17,3 = 17!/(3!14!) = 17x16x15/(3x2) = 17x8x5 = 680 different ways.

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