Answer:
a) 0.076
b) 0.5
c) 0.084
d) 0.25
e) 0.00024
f) 0.156
Step-by-step explanation:
a) In an ordinary deck there are 4 aces. The probability of getting an ace is given by:
![P=\frac{n}{N}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7Bn%7D%7BN%7D)
n: options for an ace = 4
N: total number of cards = 52
![P=\frac{4}{52}=0.076](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B4%7D%7B52%7D%3D0.076)
The probability is 7.6%
b) On the first 100 positive integers, there are 50 odd integer numbers. Then you have:
![P=\frac{50}{100}=0.5](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B50%7D%7B100%7D%3D0.5)
The probability of getting an odd number is 50%
c) From a total of 365 day in the year, May has 31 day. Then you have:
![P=\frac{31}{365}=0.084](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B31%7D%7B365%7D%3D0.084)
The probability is 8.4%
d) In this case you have two events. To get an odd number with the sum of the number of two dices you need and odd number in one dice and a pair number in the other dice.
The probability is the product of the occurrence of both events. The probability for an odd number is 1/2 and for a pair number is 1/2.
![P=P_{odd}P_{pair}=(\frac{1}{2})(\frac{1}{2})=\frac{1}{4}=0.25](https://tex.z-dn.net/?f=P%3DP_%7Bodd%7DP_%7Bpair%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%29%28%5Cfrac%7B1%7D%7B2%7D%29%3D%5Cfrac%7B1%7D%7B4%7D%3D0.25)
The probability is 25%
e) To obtain Head 6 times in a row, the probability is:
![P=\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=0.00024](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D%3D0.00024)
Probability of 0.024%
f) To get Head 4 times from 5 flights, you first calculate the probability for 1 head in five flips:
![P=(\frac{1}{2})^5=\frac{1}{32}](https://tex.z-dn.net/?f=P%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E5%3D%5Cfrac%7B1%7D%7B32%7D)
There are 5 forms of getting 4 Heads for 5 flips, then you have:
![P=5(\frac{1}{32})=\frac{5}{32}=0.156](https://tex.z-dn.net/?f=P%3D5%28%5Cfrac%7B1%7D%7B32%7D%29%3D%5Cfrac%7B5%7D%7B32%7D%3D0.156)
Te probability is 15.6%
Answer:
$28.80
Step-by-step explanation:
32 x 0.1 = 3.2
32 - 3.2 =28.8
Hope this helps :)
The airplane travels 200 mph
Step-by-step explanation:
The explanation is in the second photo
Answer:
√2726/94
Step-by-step explanation:
![cosJ=\frac{base}{hypotenuse} \\\\cosJ=\frac{KJ}{IJ} \\\\cosJ=\frac{\sqrt{29} }{\sqrt{94} } \\\\cosJ= \frac{\sqrt{29} }{\sqrt{94} } *\frac{\sqrt{94} }{\sqrt{94} } \\\\cosJ=\frac{\sqrt{2726} }{94}](https://tex.z-dn.net/?f=cosJ%3D%5Cfrac%7Bbase%7D%7Bhypotenuse%7D%20%5C%5C%5C%5CcosJ%3D%5Cfrac%7BKJ%7D%7BIJ%7D%20%5C%5C%5C%5CcosJ%3D%5Cfrac%7B%5Csqrt%7B29%7D%20%7D%7B%5Csqrt%7B94%7D%20%7D%20%5C%5C%5C%5CcosJ%3D%20%5Cfrac%7B%5Csqrt%7B29%7D%20%7D%7B%5Csqrt%7B94%7D%20%7D%20%2A%5Cfrac%7B%5Csqrt%7B94%7D%20%7D%7B%5Csqrt%7B94%7D%20%7D%20%5C%5C%5C%5CcosJ%3D%5Cfrac%7B%5Csqrt%7B2726%7D%20%7D%7B94%7D)
Hope it will help you.