select the correct answer from each drop - down menu. trey randomly selects one card a from a standard 52…

select the correct answer from each drop - down menu. trey randomly selects one card a from a standard 52 - card deck. the probability that treys card will be a heart or a black - suited card is, because the set of hearts and the set of black - suited cards are sets. reset next

select the correct answer from each drop - down menu. trey randomly selects one card a from a standard 52 - card deck. the probability that treys card will be a heart or a black - suited card is, because the set of hearts and the set of black - suited cards are sets. reset next

Answer

Explanation:

Step1: Determine number of hearts and black - suited cards

A standard deck has 52 cards. There are 13 hearts and 26 black - suited cards (13 spades and 13 clubs).

Step2: Use probability formula for mutually exclusive events

Since hearts and black - suited cards are mutually exclusive (a card can't be a heart and black - suited at the same time), the probability of event A or event B is $P(A\cup B)=P(A)+P(B)$. $P(A)=\frac{13}{52}$ (probability of getting a heart) and $P(B)=\frac{26}{52}$ (probability of getting a black - suited card). So $P(A\cup B)=\frac{13 + 26}{52}=\frac{39}{52}=\frac{3}{4}$.

Answer:

The probability that Trey's card will be a heart or a black - suited card is $\frac{3}{4}$, because the set of hearts and the set of black - suited cards are mutually exclusive sets.