A card is selected at random from a well-shuffled ordinary deck consisting of 13 spades, 13 clubs, 13 hearts, and 13 diamonds. 4 Jacks, 4 Queens, and 4 Kings are ‘face’ cards. The probability that the card is a heart or is a face card is about

(a) 0.23

(b) 0.42

(c) 0.19

(d) 0.48

(e) 0.25

b) 0.42

Step-by-step explanation:

Let A be the event that card is a heart card and B be the event that card is a face card.

We have to find P(A or B). P(A∪B)=?

P(A∪B)=P(A)+P(B)-P(A∩B)

There are 13 heart cards and  12 cards are face cards. There would be 3 face card in hearts. So,

P(A)=13/52=1/4=0.25

P(B)=12/52=3/13=0.231

P(A∩B)=3/52=0.058

P(A∪B)=0.25+0.231-0.058

P(A∪B)=0.481-0.058

P(A∪B)=0.423

So, the probability that the card is a heart or is a face card is about is 0.42.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680