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MakcuM [25]
2 years ago
6

Jason and Maria are playing a board game in which three dice are tossed to determine a player's move. Find each probability for:

P (two 5s) , P (three 5s) , and P (one 5 or two 5s).
please show work :)
Mathematics
1 answer:
fredd [130]2 years ago
6 0
Tossing a die will have 6 possible outcomes. Those are having sides that are number 1 to 6. The sample space of tossing 3 dice is equal to 6³ which is equal to 216. Now for the calculation of probabilities,

P(two 5s) = (1 x 1 x 5)/216
As we have to have the 5 in the die for two times, then for the 1 time, we can have all other numbers except 5. The answer is 5/216. 

P(three 5s) = (1 x 1 x 1)/216   = 1/216

P(one 5 or two 5s)  = (1 x 5 x 5)/216 + (1 x 1 x 5)/216 = 5/36
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The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a
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Answer:

μ=23.710740....

σ=3.592592....

Step-by-step explanation:

At first, we are told that it´s a normal distribution and the following:

P(x≤15.34)=0.1

P(x≤16.31)=0.2

We start looking for those values (0.1 and 0.2) and the probabilities that gives us those values in a normal standard distribution. There´s some tools that´ll help us out but i´ll be using a chart with the values of some probabilities in a normal standard distribution (That it´s attached).

The probability of P(z≤ a.b) where "a" is the whole part of a number and "b" the decimal part is in the coordinates (a,b). For example for our problem:

P(z≤-2.33)=0.099≈0.1

P(z≤-2.06)=0.197≈0.2

To find a probability of a normal (not standard) distribution we use a method called Normalize that proceeds:

P(x≤a)=P( (x-μ)/σ ≤ (a-μ)/σ )

Where μ is the Mean of the data and σ is the Standard deviation. P( (x-μ)/σ ≤ (a-μ)/σ ) is now part of a normal standard distribution and we are able to look for it in the chart.

We will use it to find the Mean and the STD for our distribution.

P(x≤15.34)=P(z≤-2.33)≈0.1

P(x≤16.31)=P(z≤-2.06)≈0.2

so we have the equations:

(15.34 - μ)/σ= -2.33 and (16.31 - μ)/σ= -2.06

And we solve them for μ and σ:

(15.34 - μ)/-2.33= σ and (16.31 - μ)/-2.06= σ

(15.34 - μ)/-2.33 = (16.31 - μ)/-2.06

2.06*(15.34 - μ) = 2.33(16.31 - μ)

2.33μ - 2.06μ = 2.33(16.31) - 2.06(15.34)

μ= 6.4019 / 0.27

μ= 23.710740...

With this value we find σ in one equation:

(15.34 - (23.710740...)/σ = -2.33

(15.34 - (23.710740...)/-2.33 = σ

σ=3.592592...

We finally have our answers:

μ=23.710740....

σ=3.592592....

3 0
3 years ago
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