Answer:
15/7
Step-by-step explanation:
Add the numbers put them over 7
The probability that the sum of the numbers on the balls drawn is 7 from total 5 balls without replacement = [tex]\frac{1}{5}[/tex]
Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event occurred and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
According to the question
Five balls, numbered 1, 2, 3, 4, 5, are placed in a bin.
Two balls are drawn at random without replacement.
i.e
Total possibility for drawn balls without replacement = [tex]P_{r} ^{n}[/tex]
where n = 5
r = 2
[tex]P_{r} ^{n}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
[tex]P_{2} ^{5}[/tex] = [tex]\frac{5!}{(5-2)!}[/tex]
[tex]P_{2} ^{5}[/tex] = [tex]\frac{5*4*3!}{(3)!}[/tex]
[tex]P_{2} ^{5}[/tex] = 20
Now, the probability that the sum of the numbers on the balls drawn is 7 is
(2,5) (5,2) (3,4) (4,3) = 4 possibilities in total
Therefore,
Probability = [tex]\frac{Number of favorable outcomes}{Total outcomes}[/tex]
= [tex]\frac{4}{20}[/tex]
= [tex]\frac{1}{5}[/tex]
Hence, the probability that the sum of the numbers on the balls drawn is 7 from total 5 balls without replacement = [tex]\frac{1}{5}[/tex]
To know more about probability here:
https://brainly.com/question/11234923
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