How do you work these types of problems out?
1 answer:
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Answer:
a. 0.011 or 1.1%
b. 31.56% or 0.3156
c. 99.94% or 0.9994
d. 3.42% or 0.0342
Step-by-step explanation:
Given
Number of multiple choice questions = 100
Probability of success for students who have attended lectures and done their homework = 0.85
a. Using binomial distribution
Probability of correctly answering 90 or more questions out of 100
Since,
In Binomial Distribution
where
and
Probability is therefore 1.1% or 0.011
b. Probability of correctly answering 77 to 83 questions out of 100
The probability is therefore 31.56% or 0.3156
c. Probability of correctly answering more than 73 questions out of 100
The probability is therefore 99.94% or 0.9994
d. Assuming that the student has answered randomly
Probability of success = 1/5 = 0.2
Probability of failure = 1 - 0.2 = 0.8
Probability of answering 28 or more questions correctly
The probability is therefore 3.42%
Answer:
Step-by-step explanation:
Step 1: Understanding the possible events
Selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be completed in two ways:
A. Selecting a red chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II
B. Selecting a white chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II
Therefore total probability is:
Step 2: Probability of selecting either chip from Urn I
Urn I contains 2 reds and 4 white chips, that gives a total of 6 chips.
Step 3: Probability of selecting a red chip from Urn II
Urn II originally contains 3 reds and 1 white chip, that gives a total of 4 chips.
Remember: Once a chip is added from Urn I to Urn II the total number of chips will increase in the Urn II
Case 1: When a red chip is added from Urn I to Urn II
Red chips = 4
White chips = 1
Total Chips = 5
Case 2: When a white chip is added from Urn I to Urn II
Red chips = 3
White chips = 2
Total Chips = 5
Therefore the total Probability of selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be calculated as: