Math Is Fun Forum

MKNB

Guest

Probability (3)

Question : An automatic machine fills plastic bags with a mixture of beans and vegetables. Most of the bags contain correct weight but because of the variation in size of beans and other vegetables a packet might be underweight , Overweight . A check of 4000 packets filled in the past month revealed
weights              No of packets
Under                          100
Satisfactory                 3600
Over                            300

1) What is the probability that if we select a packet  it would be satisfactory   (3600/4000)
2) Can a packet be underweight or overweight at same time

Question : Four coins are tossed simultaneously . What is  the probability distribution for number of heads.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,385

Re: Probability (3)

Question : An automatic machine fills plastic bags with a mixture of beans and vegetables. Most of the bags contain correct weight but because of the variation in size of beans and other vegetables a packet might be underweight , Overweight . A check of 4000 packets filled in the past month revealed
weights              No of packets
Under                          100
Satisfactory                 3600
Over                            300

1) What is the probability that if we select a packet  it would be satisfactory   (3600/4000)
2) Can a packet be underweight or overweight at same time

1) 3600/4000 = 36/40 = 9/10.
2) No.

Question : Four coins are tossed simultaneously . What is  the probability distribution for number of heads.

HHHH, HHHT, HHTH, HTHH, HHTT, HTTT, HTHH, HTTT, THHH, THTT etc.
All heads : 1
3 heads : 3
In a similar way, 2 heads and 1 heads can be found.
All tails would be TTTT.

At least 1 head :
1 coin : 1/2 : 0.5 : 50%;
2 coins : 3/4 : 0.75 : 75%;
3 coins : 7/8 :  0.875 : 87.5%;
4 coins : 15/16 : 0.9375 : 93.75%.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Probability (3)

Question : Four coins are tossed simultaneously . What is  the probability distribution for number of heads.

ANSWER : Write sample space
HHHH      THHH

HHHT      THHT

HHTH      THTH

HHTT      THTT

HTHH      TTHH

HTHT      TTHT

HTTH      TTTH

HTTT       TTTT

then calculate for heads
N     # outcomes with N heads     probability to get N heads

0                1                                       1/16 = 0.0625

1                4                                       4/16 = 1/4 = 0.25

2                6                                      6/16 = 3/8 = 0.375

3                4                                      4/16 = 1/4 = 0.25

4                1                                      1/16 = 0.0625

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Malik