At a church bazzar they have a game of chance that consists of picking a two digit number(0-9).You can bet 1$ by picking a two digit number
if you match two numbers you win 25$
if you match one the numbers in the same order you win 3$
if you bet 24 and 42 comes up you lose,but if 26 or 14 comes up you win
a. what is the probability of winning $18
b. what is the probability of winning 3$
c.what is the probability of losing your 1$
d.what is the expected(gain or loss) of this bazzar game
To answer these questions, we need to calculate the probabilities of each outcome. Let's break it down step by step:
a. What is the probability of winning $18?
To win $18, we need to match two numbers. There are a total of 100 possible two-digit numbers (00-99). Out of these, there are 9 favorable outcomes (11, 22, 33, 44, 55, 66, 77, 88, 99). Therefore, the probability of winning $18 is 9/100 or 0.09.
b. What is the probability of winning $3?
To win $3, we need to match one number in the same order. There are two ways this can happen: the first number matches or the second number matches. For each number, there are 10 possible outcomes (00, 01, 02, ..., 09). So, there are a total of 20 favorable outcomes. Therefore, the probability of winning $3 is 20/100 or 0.2.
c. What is the probability of losing $1?
To lose $1, we need to bet on either 24 or 42, and any other number comes up. There are two unfavorable outcomes (26, 14) out of a total of 100 possible outcomes. Therefore, the probability of losing $1 is 2/100 or 0.02.
d. What is the expected gain or loss of this bazaar game?
To calculate the expected gain or loss, we need to consider the probabilities of each outcome and their corresponding payouts.
For winning $25 by matching two numbers, the probability is 9/100 or 0.09.
For winning $3 by matching one number, the probability is 20/100 or 0.2.
For losing $1 by betting on 24 or 42, the probability is 2/100 or 0.02.
The expected gain or loss can be calculated using the formula:
(expected gain) = (probability of outcome 1 x payout of outcome 1) + (probability of outcome 2 x payout of outcome 2) + ...
(expected loss) = (-1) x (probability of losing $1)
Calculating the expected gain:
(0.09 x $25) + (0.2 x $3) + (-1 x 0.02) = $2.25 - 0.6 - 0.02 = $1.63
Therefore, the expected gain from this bazaar game is $1.63.