josie is about to draw a card at random from a standard deck of 52 playing cards. determine the probability that she will draw a red card or a 7.
a) 1/2 b) 1/13 c) 7/13 d) 15/26
thank you
pr(red or 7)=Pr(red)+Pr(7) - pr(red and 7)
= 1/2 + 4/52 - 2/52= (26+4-2)/52=28/52=7/13
there are 26 red cards (half the deck), plus two black 7's
(26 + 2)/52 ... reduce the fraction
28/52 reduces to 7/13 since both are reducible by 4 the equation to remember is P(Q/total) meaning that the probability of in this case red cards or a 7 and the total of cards goes under the Q THERE SHOULDN'T BE A PROBABILITY OVER 100%!!!!!!!
To determine the probability that Josie will draw a red card or a 7, we first need to calculate the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes:
- Red cards: There are 26 red cards in a standard deck, which consists of 13 hearts and 13 diamonds.
- 7s: There are four 7s in a standard deck, one in each suit (hearts, diamonds, clubs, spades).
To avoid double-counting the red 7s, we subtract the number of red 7s from the number of red cards. Therefore, there are 26 red cards - 2 red 7s = 24 favorable outcomes.
2. Total number of possible outcomes:
- A standard deck consists of 52 playing cards.
Now, we can determine the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 24 / 52
Simplifying the fraction:
= 6 / 13
Therefore, the probability that Josie will draw a red card or a 7 is 6/13.
The correct answer is c) 6/13.