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nataly862011 [7]
3 years ago
11

A surgical technique is performed on 10 patients. You are told there is an 80% chance of success. Find the probability that the

surgery is successful for exactly 6 patients.
Group of answer choices

0.088

0.0328

0.1208

0.9672
Mathematics
2 answers:
rodikova [14]3 years ago
7 0

<em>*100% Correct answers</em>

Question 1

A surgical technique is performed on 10 patients. You are told there is an 80% chance of success. Find the probability that the surgery is successful for exactly 6 patients.  

0.088

Question 2

Sam creates a game in which the player rolls 4 dice. What is the probability in this game of having at least 2 of the dice land on 5.  

0.13101963141  

Question 3

Katie creates a game in which 3 dimes are flipped at the same time.  

5 points are awarded if all 3 dimes land on tails, but no points are awarded for anything else. What is the probability of not getting any points? (Hint: Find the complement).  

0.875

Alex17521 [72]3 years ago
5 0

<u>Answer:</u>

<em>Probability that the surgery is successful for exactly 6 patients is 0.088.</em>

<u>Step-by-step explanation:</u>

<em>The total number of patients is 10 and the probability of success is 0.8.</em>

We have to determine the probability of success of the surgery of exactly 6 patients.

<em>6 patients can be selected from 10 patients in nC_r  ways.</em>

<em>nC_r=10C_6= \frac {10!}{6!(10-6)!}</em>

<em>= \frac{10!}{(6! \times 4!)}</em>

<em>= \frac {3628800}{(720 \times 24)}</em>

<em>=210</em>

Let us consider a combination SSSSSSFFFF where S denotes success and F denotes failure. The probability of this combination is given by

<em>0.8^6 \times 0.2^4  since the chance of success is 0.8 and chance of failure is 0.2.</em>

There are 210 such different combinations possible and the probability of every combination is the same. So we have to sum up all the probabilities to determine the final probability.

<em>Therefore the probability that surgery is successful for 6 patients is 0.8^6 \times 0.2^4 \times 210=0.088</em>

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First, you draw a green marble with a probability of 4/6

Then you draw the red one, but now there are 5 marbles in the jar (2 red ones and 3 green ones), then the probability is 2/5

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P(1) = (4/6)*(2/5) = (2/3)*(2/5) = 4/15

The probability of drawing two green marbles (X  = 2)

Again, first we draw a green marble with a probability of 4/6

Now we draw again a green marble, now there are 3 green marbles and 5 total marbles in the jar, so this time the probability is 3/5

Now we draw the red marble (there are 2 red marbles and 4 total marbles in the jar), with a probability of 2/4

The joint probability is:

P(2) = (4/6)*(3/5)*(2/4) = (2/6)*(3/5) = 1/5

The probability of drawing 3 green marbles (X = 3)

At this point you may already understand the pattern:

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