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IrinaVladis [17]
3 years ago
14

n an after school program, students must choose to either play on the playground or read a book silently. On one cloudy day, 70%

of the students chose to play on the playground, and the rest chose read a book silently. 60% of the students who went to the playground are boys, and 20% who stayed inside to read a book are boys. If a student is randomly selected on this day, what is the probability that the student is a girl?
Mathematics
1 answer:
uranmaximum [27]3 years ago
4 0
20% b/c
70% playground - 60% boys= 10%girls
100% total-70% playground = 30% inside
30% inside-20% boys= 10%girls
10%girls +10% girls=20%girls
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Rewrite the formula to find w.
sveta [45]

Answer:

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This should be the answer

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4 years ago
I have 100 items of product in stock. The probability mass function for the product's demand D is P(D=90)=P(D=100)=P(D=110)=1/3.
masya89 [10]

Answer:

The probability mass function for the items sold is

P_X(k) = \left \{ {\frac{1}{3} \, \, \, {k=90} \atop \, \frac{2}{3} \, \, \, {k=100}} \right.

The mean is 96.667

The variance is 22.222

b) The probability mass function for the unfilled demand due to lack of stock is

P_Y(k) = \left \{ {\frac{2}{3} \, \, \, {k=0} \atop \, \frac{1}{3} \, \, \, {k=10}} \right.

The mean is 3.333

The variance is 33.333

Step-by-step explanation:

If the demand is higher than 100, then you will sell 100 items only. Thus, there is a probability of 1/3+1/3 = 2/3 that you will sell 100 items, while there is a probability of 1/3 that you will sell 90.

The probability mass function for the items sold is

P_X(k) = \left \{ {\frac{1}{3} \, \, \, {k=90} \atop \, \frac{2}{3} \, \, \, {k=100}} \right.

The mean is 1/3 * 90 + 2/3 * 100 = 290/3 = 96.667

The variance is V(X) = E(X²)-E(X)² = (1/3*90² + 2/3*100²) - (290/3)² = 200/9 = 22.222

b) If order to be unfilled demand, you need to have a demand of 110, which happens with probability 1/3. In that case, the value of the variable, lets call it Y, that counts the amount of unfilled demand due to lack of stock is 110-100 = 10. In any other case, the value of Y is 0, which would happen with probability 1-1/3 = 2/3. Thus

P_Y(k) = \left \{ {\frac{2}{3} \, \, \, {k=0} \atop \, \frac{1}{3} \, \, \, {k=10}} \right.

The mean is 2/3 * 0 + 1/3 * 10 = 10/3 = 3.333

The variance is 2/3*0² + 1/3*10² = 100/3 = 33.333

4 0
3 years ago
Kyle's car repair costs $1000. He has 2 coupons which could save him $80 off of $1000, or 15% off of $1000. EXPLAIN WHICH COUPON
never [62]
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$150 is the amount the 15% coupon took off.

$850 is the amount Kyle will pay.

vs.

1000 - 80 = $920
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