n your pocket, you have 4 pennies, 3 nickels, and 6 dimes. You reach into your pocket and pull out a coin. It is either 1 penny or 1 dime. Let this event be called "A".
a) Are these events mutually exclusive? (write yes or no) _
b) Find P(A) _
c) Find (Ac) _
P(A) = 4/13 + 6/13 = ?
What is ""Ac"?
P(Ac) = 1-P(A)
To determine if events are mutually exclusive, we need to check if they can occur at the same time. In this case, the events "A" represent pulling out a coin either 1 penny or 1 dime from your pocket.
a) Are these events mutually exclusive? (write yes or no) _
No, these events are not mutually exclusive since it is possible to pull out a dime and a penny at different times from your pocket.
To find the probability of event A (P(A)), we need to count the number of favorable outcomes (pulling out a penny or a dime) and divide it by the total number of possible outcomes (the total number of coins in your pocket).
b) Find P(A) _
The number of favorable outcomes is 4 (for pulling out a penny) + 6 (for pulling out a dime) = 10.
The total number of possible outcomes is the sum of the number of pennies (4) and the number of dimes (6) = 10.
So, P(A) = favorable outcomes / total outcomes = 10 / 10 = 1.
Therefore, P(A) = 1.
To find the complement of event A (Ac), we need to consider the event that is not A. In this case, Ac represents pulling out a coin that is neither a penny nor a dime.
c) Find (Ac) _
The number of favorable outcomes for pulling out a coin that is neither a penny nor a dime is 0 (since all the remaining coins are either pennies or dimes).
Therefore, the complement of event A (Ac) has 0 favorable outcomes.
So, (Ac) = 0.